Find the Center, Transverse Axis, Vertices, Foci, and Asymptotes of the Hyperbola

question 83

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 81 } = 1$$

• A) center at \(( 0,0 )\)
• transverse axis is \(\mathrm { y }\)-axis
• vertices: \(( 0 , - 6 ) , ( 0,6 )\)
• foci: \(( - 3 \sqrt { 13 } , 0 ) , ( 3 \sqrt { 13 } , 0 )\)
• asymptotes of \(y = - \frac { 2 } { 3 } x\) and \(y = \frac { 2 } { 3 } x\)
• B) center at \(( 0,0 )\)
• transverse axis is \(\mathrm { y }\)-axis
• vertices: \(( 0 , - 6 ) , ( 0,6 )\)
• foci: \(( 0 , - 3 \sqrt { 13 } ) , ( 0,3 \sqrt { 13 } )\)
• asymptotes of \(y = - \frac { 2 } { 3 } x\) and \(y = \frac { 2 } { 3 } x\)
• C) center at \(( 0,0 )\)
• transverse axis is \(\mathrm { x }\)-axis
• vertices: \(( - 9,0 ) , ( 9,0 )\)
• foci: \(( - 3 \sqrt { 13 } , 0 ) , ( 3 \sqrt { 13 } , 0 )\)
• asymptotes of \(y = - \frac { 2 } { 3 } x\) and \(y = \frac { 2 } { 3 } x\)
• D) center at \(( 0,0 )\)
• transverse axis is \(\mathrm { y }\)-axis
• vertices: \(( - 6,0 ) , ( 6,0 )\)
• foci: \(( - 9,0 ) , ( 9,0 )\)
• asymptotes of \(y = - \frac { 2 } { 3 } x\) and \(y = \frac { 2 } { 3 } x\)

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